[en] Neoclassical transport in a toroidal plasma with finite ion orbits is studied, including for the first time the self-consistent radial electric field. Using a low-noise {delta}f particle simulation, we demonstrate that a deep electric-field well develops in a region with a steep density gradient, because of the self-collision--driven ion flux. We find that the electric field agrees with the standard neoclassical expression, when the toroidal rotation is zero, even for a steep density gradient. Ion thermal transport is modified by the electric-field well in a way which is consistent with the orbit squeezing effect, but smoothed by the finite orbits

[en] A continuum global gyrokinetic code GYRO has been developed to comprehensively simulate core turbulent transport in actual experimental profiles and enable direct quantitative comparisons to the experimental transport flows. GYRO not only treats the now standard ion temperature gradient (ITG) mode turbulence, but also treats trapped and passing electrons with collisions and finite β, equilibrium ExB shear stabilization, and all in real tokamak geometry. Most importantly the code operates at finite relative gyroradius (ρ_*) so as to treat the profile shear stabilization and nonlocal effects which can break gyroBohm scaling. The code operates in either a cyclic flux-tube limit (which allows only gyroBohm scaling) or globally with physical profile variation. Bohm scaling of DIII-D L-mode has been simulated with power flows matching experiment within error bars on the ion temperature gradient. Mechanisms for broken gyroBohm scaling, neoclassical ion flows embedded in turbulence, turbulent dynamos and profile corrugations, are illustrated

[en] A modified lattice Boltzmann algorithm is shown to have much better stability to growing temperature perturbations, when compared with the standard lattice Boltzmann algorithm. The damping rates of long-wavelength waves, which determine stability, are derived using a collisional equilibrium distribution function which has the property that the Euler equations are obtained exactly in the limit of zero time step. Using this equilibrium distribution function, we show that our algorithm has inherent positive hyperviscosity and hyperdiffusivity, for very small values of viscosity and thermal diffusivity, which are lacking in the standard algorithm. Short-wavelength modes are shown to be stable for temperatures greater than a lower limit. Results from a computer code are used to compare these algorithms, and to confirm the damping rate predictions made analytically. Finite amplitude sound waves in the simulated fluid steepen, as expected from gas dynamic theory

[en] Expressions for particle and energy fluxes and heating rates due to turbulence are derived. These fluxes and heating rates are identified from moments of an extended drift-kinetic equation for the equilibrium distribution function. These include neoclassical as well as turbulent diffusion and heating. Phase-space conservation is demonstrated, allowing the drift-kinetic equation to be expressed in conservative form. This facilitates taking moments with few approximations, mainly those consistent with drift kinetics for the equilibrium distribution function and the relative smallness of the fluctuations. The turbulent heating is uniquely defined by choosing the standard gyrokinetic definition for the energy flux. With this definition, most of the heating can be expressed in the form of ohmic heating from turbulent parallel and perpendicular current density perturbations. The latter current is identified with grad-B and curvature drifts, plus terms involving magnetic perturbations (which are smaller for low beta). A small contribution to the heating comes from the divergence of an energy flux that is dependent on the finite gyroradius of the ions. The fluxes and heating rates are expressed in a form that can be easily evaluated from gyrokinetic turbulence simulations

[en] A gyrokinetic theory of turbulent toroidal angular momentum transport as well as modifications to neoclassical poloidal rotation from turbulence is formulated starting from the fundamental six-dimensional kinetic equation. The gyro-Bohm scaled transport is evaluated from toroidal delta-f gyrokinetic simulations using the GYRO code [Candy and Waltz, J. Comput. Phys. 186, 545 (2003)]. The simulations recover two pinch mechanisms in the radial transport of toroidal angular momentum: The slab geometry ExB shear pinch [Dominguez and Staebler, Phys. Fluids B 5, 387 (1993)] and the toroidal geometry 'Coriolis' pinch [Peeters, Angioni, and Strintzi, Phys. Rev. Lett. 98, 265003 (2007)]. The pinches allow the steady state null stress (or angular momentum transport flow) condition required to understand intrinsic (or spontaneous) toroidal rotation in heated tokamak without an internal source of torque [Staebler, Kinsey, and Waltz, Bull. Am. Phys. Soc. 46, 221 (2001)]. A predicted turbulent shift in the neoclassical poloidal rotation [Staebler, Phys. Plasmas 11, 1064 (2004)] appears to be small at the finite relative gyroradius (rho-star) of current experiments

No abstract available

[en] Large ion orbits can produce nonlocal neoclassical effects on ion heat transport, the ambipolar radial electric field, and the bootstrap current in realistic toroidal plasmas. Using a global δf particle simulation, it is found that the conventional local, linear gradient-flux relation is broken for the ion thermal transport near the magnetic axis. With regard to the transport level, it is found that details of the ion temperature profile determine whether the transport is higher or lower when compared with the predictions of standard neoclassical theory. Particularly, this nonlocal feature is suggested to exist in the National Spherical Torus Experiment (NSTX) [M. Ono, S. M. Kaye, Y.-K. M. Peng et al., Nucl. Fusion 40, 557 (2000)], being consistent with NSTX experimental evidence. It is also shown that a large ion temperature gradient can increase the bootstrap current. When the plasma rotation is taken into account, the toroidal rotation gradient can drive an additional parallel flow for the ions and then additional bootstrap current, either positive or negative, depending on the gradient direction. Compared with the carbon radial force balance estimate for the neoclassical poloidal flow, our nonlocal simulation predicts a significantly deeper radial electric field well at the location of an internal transport barrier of an NSTX discharge

[en] A significant discrepancy of poloidal velocity from conventional theoretical predictions is found in global neoclassical drift-kinetic simulations of magnetic confinement fusion devices. The difference is identified as being due to the presence of large ion orbits. In the case of a large aspect ratio tokamak configuration with steep toroidal flow profiles, a novel heuristic model which estimates this nonlocal effect is presented and shown to be in good agreement with simulation results. The dominant nonlocal mechanisms captured by the model are associated with ion parallel flow modification due to the steep toroidal flow and radial electric field profiles. We compare simulation results with theoretical estimates based on the new model using profiles relevant for the National Spherical Torus Experiment. The carbon poloidal velocity observed in the simulation is in good agreement with the neoclassical theory modified by the newly identified nonlocal effects. (brief communication)

[en] Plasmas in modern tokamak experiments contain a significant fraction of impurity ions in addition to the main deuterium background ions. A new multiple ion-species δf particle simulation capability has been developed to self-consistently study the nonlocal effects of impurities on neoclassical transport in toroidal plasmas. A new algorithm for an unlike-particle collision operator, including test-particle and conserving field-particle parts, is described. Effects of the carbon impurity on the main deuterium species heat flux as well as an ambipolar radial electric field in a National Spherical Torus Experiment (NSTX) [M. Ono, S. M. Kaye, Y.-K. M. Peng et al., Nucl. Fusion 40, 557 (2000)] configuration were studied. A difference between carbon poloidal rotation found from simulation and from conventional theoretical estimates has been investigated and was identified to be a nonlocal finite orbit effect. In the case of large-aspect ratio tokamak configurations with steep toroidal flow profiles, we propose a theoretical model to describe this nonlocal effect. The dominant mechanisms captured by the model are associated with ion parallel velocity modification due to steep toroidal flow and radial electric field profiles. We present simulation results for carbon poloidal velocity in NSTX. Comparisons with neoclassical theory are discussed.

[en] It is found in collisionless Electron Temperature Gradient (ETG) turbulence simulations that, while zonal flows are weak at early times, the zonal flows continue to grow algebraically (proportional to time). These fine-scale zonal flows have a radial wave number such that krρi > 1 and krρe < 1. Eventually, the zonal flows grow to a level that suppresses the turbulence due to ExB shearing. The final electron energy flux is found to be relatively low. These conclusions are based on particle convergence studies with adiabatic ion electrostatic flux-tube gyrokinetic δf particle simulations run for long times. The Rosenbluth-Hinton random walk mechanism is given as an explanation for the long time build up of the zonal flow in ETG turbulence and it is shown that the generation is (k perpendicular ρe)2 smaller than for isomorphic Ion Temperature Gradient (ITG) problem. This mechanism for zonal flow generation here is different than the modulational instability mechanism for ITG turbulence. These results are important because previous results indicated zonal flows were unimportant for ETG turbulence. Weak collisional damping of the zonal flow is also shown to be a n important effect